1. 10/06/2003LSC WIDE COLLOQUIUM1 LSC Pulsar Group and P Shawhan, S Marka, and S Koranda presented by B Allen, R Dupuis, N Christensen, and X Siemens S2 Hardware Pulsar Injections

2. 10/06/2003LSC WIDE COLLOQUIUM2 Why Do Hardware Injections? Provides end-to-end validation of search code: –Gain confidence about tricky things like floating point dynamic range in filtering process –Helps algorithm/code developers in testing –Provide a fixed point of reference to return to Challenges in the pulsar case: –Realistic signals must last for hours (~10 7 cycles). This is unlike the burst (seconds) and inspiral (tens of seconds) case. –Would like to avoid the “SB” scenario where the simulated signal dominates the data –Getting the correct initial phase relationship at the different detector sites can be tricky (specifics later) Simpler in pulsar case: –Calibration: signal is at a “single” frequency

3. 10/06/2003LSC WIDE COLLOQUIUM3 S2 Pulsar Injection Parameters Signal is sum of two different pulsars, P1 and P2 P1: Constant Intrinsic Frequency Sky position: 0.3766960246 latitude (radians) 5.1471621319 longitude (radians) Signal parameters are defined at SSB GPS time 733967667.026112310 which corresponds to a wavefront passing: LHO at GPS time 733967713.000000000 LLO at GPS time 733967713.007730720 In the SSB the signal is defined by f = 1279.123456789012 Hz fdot = 0 phi = 0 A+ = 1.0 x 10 -21 Ax = 0 [equivalent to iota=pi/2] P2: Spinning Down Sky position:1.23456789012345 latitude (radians) 2.345678901234567890 longitude (radians) Signal parameters are defined at SSB GPS time: SSB 733967751.522490380, which corresponds to a wavefront passing: LHO at GPS time 733967713.000000000 LLO at GPS time 733967713.001640320 In the SSB at that moment the signal is defined by f=1288.901234567890123 fdot = -10 -8 [phase=2 pi (f dt+1/2 fdot dt^2+...)] phi = 0 A+ = 1.0 x 10 -21 Ax = 0 [equivalent to iota=pi/2]

4. 10/06/2003LSC WIDE COLLOQUIUM4 How was simulated signal made? 12 hours of strain data was produced (with overall 10 21 normalization factor) using LAL routines: 144 files (5 minutes each) were produced. Each file contains 16384*300+1 4-byte IEEE 754 floats: –Key1234.5(4 bytes) –Sample 0xxxxxx(4 bytes) –Sample 1 yyyyyy(4 bytes) –… Time range was 00:00 –12:00 UTC April 10th The 2.8 GB of injection data was shipped to each site More details of signals in LIGO DCC: LIGO-G030479-00-Z S2_pulsar_LHO_733968013.dat S2_pulsar_LHO_733968313.dat S2_pulsar_LHO_733968613.dat … and so on.

5. 10/06/2003LSC WIDE COLLOQUIUM5 Simulated strain: Detector Response Function April 10 th 04:00 UTC is: LHO: 8 pm April 9 th LLO: 10 pm April 9 th April 10 th 10:00 UTC is: LHO: 2 am April 10 th LLO: 4 am April 10 th simulated source is passing near a zero of the antenna pattern.

6. 10/06/2003LSC WIDE COLLOQUIUM6 How and When? More than 9 hours of pulsar injections into L1, H1 and H2 –Start 18:19 PDT on April 9 –Stop 04:03 PDT on April 10 Instruments were in lock for almost the entire time Pulsar plus calibration line summed into DARM_CTRL ETM_X and ETM_Y used for other injections Strain/DARM_CTRL calibrations worked out at 1284 Hz, halfway between two signals. NOTE: THESE WERE SUBSEQUENTLY REVISED FOR H1 AND H2 – SO AT THOSE DETECTORS THE OVERALL STRAIN FACTOR WAS NOT 1.e-21! Injections started at 733974613 (01:50:00 UTC April 10) and continued until 734007889 (11:04:36 UTC April 10) with some minor interruptions (loss of lock, realignment, computer restarted because of lack of memory).

7. 10/06/2003LSC WIDE COLLOQUIUM7 Time Domain Bayesian Analysis For each signal all parameters were successfully inferred (except a constant 90 degrees phase shift) Four plots were produced for each signal: 1.posterior probability density function of h 0 given the data (marginalized over the other parameters) 2.confidence contour plot of \cos\iota vs h 0 with levels at 67%, 95%, 99%, and 99.9% 3.confidence contour plot of polarisation angle \psi vs h 0 with levels at 67%, 95%, 99%, and 99.9% 4.confidence contour plot of phase \phi_0 vs h 0 with levels at 67%, 95%, 99%, and 99.9% Coherent analysis using data from all sites showed that phase was conserved between sites Full results (with larger images) are posted at http://www.astro.gla.ac.uk/users/rejean/lsc/S2injections (lsc/lsconly) http://www.astro.gla.ac.uk/users/rejean/lsc/S2injections

8. 10/06/2003LSC WIDE COLLOQUIUM8 Results for signal P1 L1: p(h 0 | B k ) p(h 0,cos  | B k )p(h 0,  0 | B k ) p(h 0,  | B k ) H1: H2:

9. 10/06/2003LSC WIDE COLLOQUIUM9 Results for signal P2 p(h 0 | B k ) p(h 0,cos  | B k )p(h 0,  0 | B k ) p(h 0,  | B k ) L1: H1: H2:

10. 10/06/2003LSC WIDE COLLOQUIUM10 Joint Coherent Analysis p(a|all data) = p(a|H1) p(a|H2) p(a|L1) Signal P1Signal P2 individual IFOs all IFOs

11. 10/06/2003LSC WIDE COLLOQUIUM11 4 and 5 Parameter Search Works Well And Has Been Tested Parameters : f 0, cos(i), y, h 0, and then df Tested on synthesized data (4 and 5 parameters) Tested on the S2 Injected Signals (4 parameters) Use likelihood and priors of the time-domain search as MCMC starting point. df uncertain to 1/60 Hz. For a 5 Hz search, run on 300 nodes 10 hours cpu for 10 days of data Markov Chain Monte Carlo Results

12. 10/06/2003LSC WIDE COLLOQUIUM12 4 Parameters: S2 Injection: It Works! Signal 1 as seen in H1 above. Exact match with time domain search. Full results posted at http://physics.carleton.edu/Research/ligo/S2injectCW.html Found h 0, , and cos , but   off due presumably to a time definition

13. 10/06/2003LSC WIDE COLLOQUIUM13 Signal 1 at H1 Signal 1: Parameters of injected signal: RA = 5.1471621319 rad DEC = 0.3766960246 rad f0 = 1279.123456789012 Hz fdot = 0.0 psi = 0.0 phi=0.0 cos(iota)=0.0 h0 = 2.0e-21 (± calibration errors) MCMC Result (h0 scaled by 10-22) The Statistics Are: Mean Standard Deviation h0 20.97711 1.44419 psi -0.02704 0.02424 phi -0.66802 0.03438 cosiota -0.04865 0.02474 Quantiles for each variable: 2.5% 97.5% h0 18.17624 23.817896 psi -0.07318 0.019197 phi -0.73427 -0.601182 cosiota -0.09867 -0.001396

14. 10/06/2003LSC WIDE COLLOQUIUM14 Signal 2 at L1 Signal 1 as seen in L1 above. Exact match with time domain search.

15. 10/06/2003LSC WIDE COLLOQUIUM15 Signal 1 at L1 Signal 1: Parameters of injected signal: RA = 5.1471621319 rad DEC = 0.3766960246 rad f0 = 1279.123456789012 Hz fdot = 0.0 psi = 0.0 phi=0.0 cos(iota)=0.0 h0 = 2.0e-21 (± calibration errors) MCMC Results (h0 scaled by 10-22) The statistics are: Mean Standard Deviation h0 19.00456 1.44050 psi -0.08483 0.03439 phi -0.82187 0.04071 cosiota -0.07484 0.03583 Quantiles for each variable: 2.5% 97.5% h0 16.2522 21.889774 psi -0.1460 -0.011781 phi -0.9026 -0.743842 cosiota -0.1473 -0.005469

16. 10/06/2003LSC WIDE COLLOQUIUM16 Signal 2 at H2 Signal 2 as seen in H2 above. Exact match with time domain search.

17. 10/06/2003LSC WIDE COLLOQUIUM17 Signal 2 at H2 Signal 2: Parameters of injected signal: RA = 2.345678901234567890 DEC = 1.23456789012345 f0 = 1288.901234567890123 Hz fdot = -1.0e-8 Hz/s psi = 0.0 h0 = 2.0e-21 (± calibration errors) phase = 0.0 cos(iota)=0.0 MCMC Results (h0 scaled by 10-22) The statistics are: Mean SD h0 19.132891 0.91848 psi -0.008155 0.02172 phi -0.753110 0.02425 cosiota 0.061423 0.02135 Quantiles for each variable: 2.5% 97.5% h0 17.24495 21.02338 psi -0.05211 0.03266 phi -0.80178 -0.70678 cosiota 0.02091 0.10527

18. 10/06/2003LSC WIDE COLLOQUIUM18 6 Parameter Search: Road to a SN1987A Search Parameters : df, dfdot, f 0, cos(i), psi, and h 0 Test on synthesized data has commenced Different Technique - “Delayed Rejection in Reversible Jump Metropolis-Hastings”, plus other tricks. Will soon test on S2 injected signal 2 where dfdot is non-zero New manpower - John Veitch @ Glasgow

19. 10/06/2003LSC WIDE COLLOQUIUM19 Generated PDFs from the parameters h 0, df, and dfdot. In this example from the 6 parameter problem the true values for the critical parameters were h 0 =10.0, df = 0.0078125, and dfdot = 2x10 -10. The priors we uniform -10 -9 Hz/s<dfdot<10 -9 Hz/s and -1/60 Hz < df < 1/60 Hz 6 Parameter Search

20. 10/06/2003LSC WIDE COLLOQUIUM20 S2 Frequency Domain Injection Results The signal in the data (green 60s SFTs, red 1800s SFTs) Signal I Signal II Hz

21. 10/06/2003LSC WIDE COLLOQUIUM21 Results

22. 10/06/2003LSC WIDE COLLOQUIUM22 Still have problems with phase of the signal … 1800s SFTs (which I did not show results for) have equally good results (they are calibrated with calibration factors averaged every 30 mins) Overall results are very encouraging FD Conclusions

23. 10/06/2003LSC WIDE COLLOQUIUM23 What about S3? The Pulsar Group will to provide a fast real- time function that can be called, which will return h(t). Will be used to do pulsar injections during entire S3 run (~5 pulsars, parameters TBD). Uta Weiland (GEO Hannover) is writing a routine for this purpose for GEO pulsar injections. Can only inject 1 pulsar.